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Abstract: We study critical behavior in gravitational collapse of a general spherically
symmetric Yang-Mills field coupled to the Einstein equations. Unlike the
magnetic ansatz used in previous numerical work, the general Yang-Mills
connection has two degrees of freedom in spherical symmetry. This fact changes
the phenomenology of critical collapse dramatically. The magnetic sector
features both type I and type II critical collapse, with universal critical
solutions. In contrast, in the general system type I disappears and the
critical behavior at the threshold between dispersal and black hole formation
is always type II. We obtain values of the mass scaling and echoing exponents
close to those observed in the magnetic sector, however we find some
indications that the critical solution differs from the purely magnetic
discretely self-similar attractor and exact self-similarity and universality
might be lost. The additional "type III" critical phenomenon in the magnetic
sector, where black holes form on both sides of the threshold but the
Yang-Mills potential is in different vacuum states and there is a mass gap,
also disappears in the general system. We support our dynamical numerical
simulations with calculations in linear perturbation theory; for instance, we
compute quasi-normal modes of the unstable attractor (the Bartnik-McKinnon
soliton) in type I collapse in the magnetic sector.